Solve for $x$ and $y$ using elimination. ${5x-3y = 7}$ ${2x+3y = 28}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $7x = 35$ $\dfrac{7x}{{7}} = \dfrac{35}{{7}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-3y = 7}\thinspace$ to find $y$ ${5}{(5)}{ - 3y = 7}$ $25-3y = 7$ $25{-25} - 3y = 7{-25}$ $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ You can also plug ${x = 5}$ into $\thinspace {2x+3y = 28}\thinspace$ and get the same answer for $y$ : ${2}{(5)}{ + 3y = 28}$ ${y = 6}$